Modified boundary integral formulations for the Helmholtz equation

Abstract In this paper we describe some modified regularized boundary integral equations to solve the exterior boundary value problem for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. We formulate combined boundary integral equations which are uniquely solvable for all wave numbers even for Lipschitz boundaries Γ = ∂ Ω . This approach extends and unifies existing regularized combined boundary integral formulations.

[1]  X. Antoine,et al.  Alternative integral equations for the iterative solution of acoustic scattering problems , 2005 .

[2]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  W. Benthien,et al.  Nonexistence and Nonuniqueness Problems Associated with Integral Equation Methods in Acoustics , 1997 .

[4]  Olaf Steinbach,et al.  Numerische Näherungsverfahren für elliptische Randwertprobleme , 2003 .

[5]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[6]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[7]  S. Amini.  On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem , 1990 .

[8]  P. Harris,et al.  A comparison between various boundary integral formulations of the exterior acoustic problem , 1990 .

[9]  R. Kress,et al.  On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation , 1983 .

[10]  R. E. Kleinman,et al.  Boundary Integral Equations for the Three-Dimensional Helmholtz Equation , 1974 .

[11]  Peter Werner,et al.  Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung , 1965 .

[12]  Ralf Hiptmair,et al.  Regularized Combined Field Integral Equations , 2005, Numerische Mathematik.

[13]  Olaf Steinbach,et al.  A fast multipole boundary element method for a modified hypersingular boundary integral equation , 2003 .

[14]  W. McLean.  Strongly Elliptic Systems and Boundary Integral Equations , 2000 .